1. What is a model?

There have been many attempts to define models and their role in
archaeological research, for example:

'Models or hypotheses express the relationships between the
variables that comprise our theoretical framework'(Hole 1973, 31),

'A model is an object ... which is similar to another one and
which is studied instead because the latter is too complicated or
inaccessible'(Klejn 1973, 705),

'Most models ... are simple, and a good model is one which,
although simple in itself, will bring forth a range of varied
forms, most of which achieve a close correspondence with part of
the observed data' (Renfrew 1979,
30),

'The common denominator for all definitions is that a model is a
partial and/or simplified representation of something else' (Voorrips 1987, 68).

What all these (and many other) definitions seem to have in common is
that a model is a simplified representation of some sort of reality,
whether that be a physical object, an event, a process, or our own
thought processes. There is also a common theme that models are needed
in order to enable us to come to grips with the complexity of the
reality that we are studying or to which we relate in some way. For
example, we use models known as railway timetables as a simplified
representation of the operation of a railway system, because we would
never be able to cope with the full complexity of such a system.

We can also begin to see, even at this early stage, signs of a
divergence in views of the role or purpose of models. On the one hand,
we have models which are used as a 'bridge' between the world of
theory and the 'real world', and which act as tools and enable the two
to interact. They can even be seen as necessary mediators between
these two worlds, without which we cannot engage properly with our
data (Orton 2000, 10). On the
other hand, we have models, which, although clearly falling within the
above definitions, are more of an end in themselves. This difference
might be seen as a division between 'tactical' and 'strategic' (Orton 1973), or as a difference
between disciplines, with (for example) statisticians tending towards
the former usage and archaeologists towards the latter. This is a
point to which I shall return in more detail once we have narrowed the
definition to mathematical models and considered what it is that we
might wish to model.